Finite Group Databasebeta

← #14770234

Subgroups — #14770234

Order 2816.

1246 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623094C211yesmaximal, characteristic
2D4×C4⋊Dic11C211yesmaximal, characteristic, complemented
3#13069577C211yesmaximal, characteristic, complemented
4#13069563C211yesmaximal, characteristic, complemented
5#13069054C212yesmaximal, complemented
6#13068931C212yesmaximal, complemented
7#13068712C212yesmaximal, complemented
8#13068617C211yesmaximal, characteristic, complemented
9C4×#66885C211yesmaximal, characteristic, complemented
10#13068336C212yesmaximal, complemented
11C2×C11×#436C211yesmaximal, characteristic, complemented
12C22×C11×M16C2212yes—
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66991—21no—
15C2×D4×Dic11—21no—
16C2×#66983C2212yes—
17C2×#66979C2212yes—
18C22×C4⋊Dic11C2212yes—
19#10623094—24no—
20#10623094C418yescomplemented
21C2×#66945—21no—
22C2×#66938—22no—
23C2×C4×D44C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C11×#436—24no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2212yes—
28C2×C4×C8×C11C2211yescharacteristic
29#10622825C2212yes—
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66885C2212yes—
33#10622598—21no—
34#10622563—22no—
35#10622548C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37#10622189C2212yes—
38#10622189C2212yes—
39#10622189C2211yescharacteristic
40#10622189C2212yes—
41#10622189C2212yes—
42#10622189C2211yescharacteristic
43#10622189C2212yes—
44C22×D4×C11D411yescharacteristic
45C23×C4×C11C2312yes—
46C22×C22⋊D11—22no—
47C23×Dic11—22no—
48C22×D44C2311yescharacteristic
49C22×C4×D11—21no—
50C22×Dic22—21no—
51C2×C11×M16—24no—
52C2×C11×M16—24no—
53C2×C11×M16—42no—
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2312yes—
56C22×C8×C11C2311yescharacteristic
57C4×D4×C11C2×C414yes—
58C4×D4×C11D414yes—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C22⋊C4D412yes—
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—22no—
64#66991—28no—
65D4×Dic11—44no—
66#66983—24no—
67#66983C2×C418yescomplemented
68C2×(C2×D11)⋊C4—21no—
69C2×(C2×D11)⋊C4—22no—
70#66979—24no—
71#66979C2×C418yescomplemented
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—24no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—42no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2312yes—
80C2×C4⋊Dic11C2312yes—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4×Dic11—22no—
84C2×C4×Dic11—21no—
85#66945—28no—
86#66938—216no—
87C4×D44—22no—
88C4×D44C2×C414yescomplemented
89#66922—22no—
90#66922C2×C414yescomplemented
91C11×C4⋊C8—22no—
92C11×C22⋊C8—24no—
93C4×C8×C11—22no—
94C11⋊#95—21no—
95C11⋊#95—22no—
96#66885—22no—
97#66885—22no—
98#66885—42no—
99#22503—111nomaximal, Sylow
100C24×C11C2×D412yes—
101C23×D11—21no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11C22⋊C414yes—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11C22×C414yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D414yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2411yescharacteristic
115C2×C22⋊D11—28no—
116C2×C22⋊D11—82no—
117C2×C22⋊D11—82no—
118C22×Dic11—21no—
119C22×Dic11—21no—
120C22×Dic11—22no—
121C22×Dic11—21no—
122C22×Dic11—22no—
123C22×Dic11—44no—
124C22×Dic11—44no—
125C22×Dic11—82no—
126C2×D44—21no—
127C2×D44—21no—
128C2×D44—21no—
129C2×D44—21no—
130C2×D44—21no—
131C2×D44C22×C412yes—
132C2×C4×D11—24no—
133C2×C4×D11—42no—
134C2×C4×D11—42no—
135C2×Dic22—24no—
136C2×Dic22—81no—
137C2×Dic22—81no—
138C11×M16—48no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11—22no—
142C2×C8×C11—21no—
143C2×C8×C11—22no—
144C2×C8×C11—21no—
145C2×C8×C11—22no—
146C2×C8×C11—21no—
147C2×C8×C11#4112yes—
148C11×C4⋊C4C22⋊C414yes—
149C11×C22⋊C4C22⋊C418yes—
150C42×C11C22×C412yes—
151C42×C11C2×D412yes—
152C22⋊Dic11—28no—
153C22⋊Dic11—44no—
154(C2×D11)⋊C4—24no—
155(C2×D11)⋊C4—28no—
156C4⋊Dic11—24no—
157C4⋊Dic11—22no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—22no—
161C4⋊Dic11—21no—
162C4⋊Dic11—22no—
163C4⋊Dic11—21no—
164C4⋊Dic11—44no—
165C4⋊Dic11—42no—
166C4⋊Dic11—81no—
167C4⋊Dic11C22×C414yes—
168C4⋊Dic11C22×C412yes—
169C4⋊Dic11#4112yes—
170C4×Dic11—28no—
171C4×Dic11—42no—
172C2×#555—111no—
173C2×#436D1111yescharacteristic, complemented
174D4×C4⋊C4—111no—
175#1990—111no—
176#1987—111no—
177#1895—112no—
178#1874—112no—
179#1825—112no—
180#1802—111no—
181C4×#102—111no—
182#1736—112no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11C2×C22⋊C414yes—
190C23×C11C22×D411yescharacteristic
191C22×D11—22no—
192C22×D11—41no—
193C22×D11—41no—
194C22×D11—41no—
195C22×D11—41no—
196C22×D11—41no—
197C22×D11—41no—
198D4×C11—28no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11C2×C22⋊C414yes—
208C2×C4×C11C2×C22⋊C412yes—
209C2×C4×C11C2×C22⋊C412yes—
210C2×C4×C11AGL(1,ℤ/8)12yes—
211C2×C4×C11#13712yes—
212C2×C4×C11C23×C411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11H(5,𝔽2)11yescharacteristic
217C2×C4×C112−1+411yescharacteristic
218C22⋊D11—88no—
219C2×Dic11—22no—
220C2×Dic11—24no—
221C2×Dic11—22no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—42no—
226C2×Dic11—41no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—41no—
234C2×Dic11—88no—
235D44—22no—
236D44—22no—
237D44—41no—
238D44—41no—
239C4×D11—48no—
240Dic22—84no—
241C8×C11—22no—
242C8×C11—42no—
243C8×C11—41no—
244C22×M16C2×D1112yes—
245#555—118no—
246#555—224no—
247C2×C4⋊Q8—111no—
248C2×#124—222no—
249C2×#121—112no—
250C2×#121—221no—
251C2×C4×D4—111no—
252C2×C4×D4—221no—
253C2×C4×D4C2×D1111yescharacteristic
254C2×#117—112no—
255C2×#117—221no—
256C22×C4⋊C4—112no—
257#436—24no—
258C2×C4⋊C8C2×D1111yescharacteristic
259C2×#102—111no—
260C2×#102—111no—
261C2×#102—112no—
262C2×C22⋊C8C2×D1112yes—
263C2×C4×C8C2×D1111yescharacteristic
264#389—221no—
265#385—222no—
266#384—111no—
267#380—112no—
268C4×C4⋊C4—111no—
269#340—112no—
270#340—111no—
271#340—112no—
272#340—112no—
273#340—112no—
274#340—112no—
275#340—111no—
276C22×C11—24no—
277C22×C11—24no—
278C22×C11—24no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11C22×C22⋊C411yescharacteristic
284C22×C11#54611yescharacteristic
285C22×C11#54711yescharacteristic
286C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
287C22×C11C2×#13711yescharacteristic
288C22×C11#57611yescharacteristic
289C22×C11#57711yescharacteristic
290C2×D11—42no—
291C2×D11—42no—
292C2×D11—42no—
293C2×D11—81no—
294C2×D11—81no—
295C2×D11—81no—
296C2×D11—81no—
297C4×C11—24no—
298C4×C11—22no—
299C4×C11#41714yes—
300C4×C11C4×#4111yescharacteristic
301C4×C11#52011yescharacteristic
302C4×C11#54611yescharacteristic
303C4×C11#54711yescharacteristic
304Dic11—42no—
305Dic11—44no—
306Dic11—42no—
307Dic11—81no—
308Dic11—82no—
309C22×Q8—221no—
310C22×D4—111no—
311C22×D4—222no—
312C22×D4D4411yescharacteristic
313C23×C4—221no—
314C23×C4—222no—
315C23×C4C22×D1112yes—
316C2×M16—24no—
317C2×M16—24no—
318C2×M16—42no—
319C22×C8C22×D1112yes—
320C22×C8C22×D1111yescharacteristic
321C22×C8C22×D1111yescharacteristic
322C4⋊Q8—114no—
323C4⋊Q8—222no—
324#124—2216no—
325#121—118no—
326#121—228no—
327#121—224no—
328C4×D4—114no—
329C4×D4—222no—
330C4×D4—444no—
331C4×D4C4×D1114yes—
332C4×D4C22⋊D1114yes—
333#117—118no—
334#117—224no—
335#117—228no—
336C2×C4⋊C4—111no—
337C2×C4⋊C4—111no—
338C2×C4⋊C4—112no—
339C2×C4⋊C4—112no—
340C2×C4⋊C4—111no—
341C2×C4⋊C4—224no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4—222no—
344C2×C4⋊C4—221no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4—442no—
347C2×C4⋊C4D4411yescharacteristic
348C2×C22⋊C4—222no—
349C2×C22⋊C4—222no—
350C2×C22⋊C4—221no—
351C2×C22⋊C4—222no—
352C2×C22⋊C4D4412yes—
353C2×C42—222no—
354C2×C42—221no—
355C2×C42C22×D1111yescharacteristic
356C4⋊C8—22no—
357#102—222no—
358#102—222no—
359#102—442no—
360C22⋊C8—24no—
361C4×C8—22no—
362#95—221no—
363#95—222no—
364C2×C11—44no—
365C2×C11#233911yescharacteristic
366C2×C11C2×#41711yescharacteristic
367C2×C11#289711yescharacteristic
368C2×C11#332511yescharacteristic
369C2×C11#332911yescharacteristic
370C2×C11#335411yescharacteristic
371C2×C11#335711yescharacteristic
372D11—82no—
373C24—221no—
374C24C2×D4412yes—
375C2×Q8—224no—
376C2×Q8—881no—
377C2×Q8—881no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—112no—
381C2×D4—228no—
382C2×D4—221no—
383C2×D4—221no—
384C2×D4—221no—
385C2×D4—221no—
386C2×D4—221no—
387C2×D4—882no—
388C2×D4—882no—
389C2×D4(C2×D11)⋊C414yes—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—221no—
395C22×C4—221no—
396C22×C4—222no—
397C22×C4—224no—
398C22×C4—221no—
399C22×C4—222no—
400C22×C4—444no—
401C22×C4—442no—
402C22×C4—442no—
403C22×C4—444no—
404C22×C4—882no—
405C22×C4C2×C4×D1114yes—
406C22×C4C2×D4412yes—
407C22×C4C2×D4411yescharacteristic
408C22×C4C2×D4411yescharacteristic
409C22×C4C2×C22⋊D1114yes—
410C22×C4C23×D1111yescharacteristic
411M16—48no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—22no—
420C2×C8#434112yes—
421C4⋊C4—112no—
422C4⋊C4—114no—
423C4⋊C4—112no—
424C4⋊C4—224no—
425C4⋊C4—221no—
426C4⋊C4—221no—
427C4⋊C4—222no—
428C4⋊C4—221no—
429C4⋊C4—222no—
430C4⋊C4—222no—
431C4⋊C4—221no—
432C4⋊C4—444no—
433C4⋊C4—442no—
434C4⋊C4—881no—
435C4⋊C4(C2×D11)⋊C414yes—
436C22⋊C4—228no—
437C22⋊C4—228no—
438C22⋊C4—224no—
439C22⋊C4—444no—
440C22⋊C4(C2×D11)⋊C418yes—
441C42—228no—
442C42—442no—
443C42C2×C4×D1112yes—
444C42C2×C22⋊D1112yes—
445C11#2250311yescharacteristic, complemented, Sylow
446C23—22no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—22no—
451C23—22no—
452C23—222no—
453C23—441no—
454C23—441no—
455C23—441no—
456C23—441no—
457C23—441no—
458C23—441no—
459C23C2×(C2×D11)⋊C414yes—
460C23C22×D4411yescharacteristic
461Q8—884no—
462D4—28no—
463D4—222no—
464D4—222no—
465D4—441no—
466D4—441no—
467D4—888no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—222no—
477C2×C4—224no—
478C2×C4—222no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—442no—
483C2×C4—441no—
484C2×C4—442no—
485C2×C4—448no—
486C2×C4—441no—
487C2×C4—442no—
488C2×C4—441no—
489C2×C4—442no—
490C2×C4—442no—
491C2×C4—441no—
492C2×C4—888no—
493C2×C4#6696112yes—
494C2×C4#6696212yes—
495C2×C4C2×(C2×D11)⋊C414yes—
496C2×C4C2×(C2×D11)⋊C412yes—
497C2×C4C2×(C2×D11)⋊C412yes—
498C2×C4C22×C4×D1111yescharacteristic
499C2×C4C2×#434111yescharacteristic
500C2×C4#6703711yescharacteristic
501C2×C4#41×D1111yescharacteristic
502C2×C4#6704311yescharacteristic
503C2×C4C22×C22⋊D1111yescharacteristic
504C8—22no—
505C8—42no—
506C8—41no—
507C22—24no—
508C22—24no—
509C22—24no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—442no—
515C22—442no—
516C22—442no—
517C22—881no—
518C22—881no—
519C22—881no—
520C22—881no—
521C22#1062308511yescharacteristic
522C22#1062308611yescharacteristic
523C22C2×#6696111yescharacteristic
524C22C2×#6696211yescharacteristic
525C22#1062328211yescharacteristic
526C22#1062328311yescharacteristic
527C22C22×(C2×D11)⋊C411yescharacteristic
528C4—24no—
529C4—22no—
530C4—442no—
531C4—442no—
532C4—444no—
533C4—882no—
534C4—881no—
535C4#1062274614yes—
536C4C4×#434111yescharacteristic
537C4#1062307711yescharacteristic
538C4#1062333711yescharacteristic
539C4#1062335511yescharacteristic
540C2—44no—
541C2—882no—
542C2#1307144111yescharacteristic
543C2C2×#1062274611yescharacteristic
544C2#1307714311yescharacteristic
545C2#1308085911yescharacteristic
546C2#1308091111yescharacteristic
547C2#1308121211yescharacteristic
548C2#1308124311yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#436C2
socleC23×C11C22×D4
prime radicalC2×#10623094C2
cosocleC22×C4×C11C24
hypercenterC2×#436D11
hypocenterC11#22503
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#436

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. D4×C4⋊Dic11C2semidirect
3. #13069577C2semidirect
4. #13069563C2semidirect
5. #13069054C2semidirect
6. #13068931C2semidirect
7. #13068712C2semidirect
8. #13068617C2semidirect
9. C4×#66885C2semidirect
10. #13068336C2semidirect
11. C2×C11×#436C2semidirect
20. #10623094C4semidirect
67. #66983C2×C4semidirect
71. #66979C2×C4semidirect
88. C4×D44C2×C4semidirect
90. #66922C2×C4semidirect
173. C2×#436D11semidirect
445. C11#22503semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106230942
D4×C4⋊Dic112
#130695772
#130695632
#130690542
#130689312
#130687122
#130686172
C4×#668852
#130683362
C2×C11×#4362
#2250311